To form a hydrogen atom, a proton is fixed at a point and an electron is brought from far away to a distance of 0.529 × 10−10 m, the average distance between proton and electron in a hydrogen atom. How much work is done?

Given Information:

distance between electron and proton = d = 0.529x10⁻¹⁰ m

charge on electron = q₁ = -1.60x10⁻¹⁹ C

charge on proton = q₂ = 1.60x10⁻¹⁹ C

Required Information:

Work done = W = ?

Work done = 4.35x10⁻¹⁸ Joules

Explanation:

We know that work done is given by

Work done = kq₁q₂/r

Where q₁ is the charge on electron, q₂ is the charge on proton and k is the coulomb constant and its value is 9x10⁹ Nm²/C²

Work done = (9x10⁹*-1.60x10⁻¹⁹*1.60x10⁻¹⁹)/0.529x10⁻¹⁰

Work done = 4.35x10⁻¹⁸ Joules

Therefore, 4.35x10⁻¹⁸ Joules of work is required to bring electron from a distance of 0.529x10⁻¹⁰ m towards the proton to form a hydrogen atom.